Complexity Theory is the study of how order, patterns, and structure appear in complex, apparently chaotic systems that are far from equilibrium, sharing matter and energy (of low entropy) with their environment and exhibiting "self-organization" and stability, apparently avoiding the degradation (increase of entropy) normally required by the second law of thermodynamics.

Many scientists had known for decades before Bertalanffy that living systems somehow avoid the inevitable degradation suffered by physical systems, according to the second law of thermodynamics. Instead of approaching thermodynamic equilibrium (complete chaos and maximum entropy, living systems maintain themselves in a high state of order (or information) far from equilibrium. Earlier thinkers had called this a "dynamic equilibrium," but Bertalannfy called it "flow equilibrium." In his 1932 book Theoretische Biologie, he described living systems as open systems that exchange matter and energy with the environment.

More important than the new terminology, Bertalanffy in 1940 described what was happening in a way made famous five years later by Erwin Schrödinger in his book What is Life?, namely that energy is not enough, it must be energy with low (or negative) entropy, or what Bertalanffy correctly called "free energy.".

Bertalanffy wrote:

In open systems we have not only production of entropy due to irreversible processes, but also import of negative entropy. This is the case in the living organism which imports [consumes nutrients with] complex molecules that are high in free energy. Thus, living systems, maintaining themselves in a steady state, can avoid the increase of entropy, and may even
develop towards states of increased order and organization.

Uncommon Sense, The Life and Thought of Ludwig von Bertalanffy (1983), p.83)

In his 1945 essay What is Life?, Schrödinger would say that "life feeds on negative entropy." Schrödinger described this as "order out of order" that distinguishes life from the "order out of chaos" exhibited by many complex physical systems studied today.

Ilya Prigogine and his collaborator Isabel Stengers titled their 1984 book Order Out Of Chaos. In it, they focused on physical systems far from equilibrium which exhibit the flow of matter and energy from the environment through an open system. Prigogine called them "dissipative structures" and developed the non-linear thermodynamics needed to describe them mathematically.

Prigogine believed that before him, there was "no direction of time, no distinction between past and future," because even quantum mechanics, in the form of Erwin Schrödinger's deterministic wave equation, could not do so (without invoking a collapse of the wave function). Prigogine introduced what he called a "third time" into physics - time as irreversibility. He saw non-equilibrium, dissipative systems far from equilibrium, as a new source of order giving to the system ill-defined "new space-time properties." ("The Meaning of Entropy," in Evolutionary Epistemology, p.63)

In the 1950's and 1960's, American meteorologist Edward Lorenz found that small rounding errors in his computer data (which has a limited number of significant figures) leads to large non-linear instabilities that expand exponentially in time and make long-term prediction impossible. This is the famous "Butterfly wings in Beijing" effect discovered in weather predictions.

Lorenz's work led to the mathematical theory of deterministic chaos, a central component of modern complexity theory. Lorenz had discovered that deterministic and linear dynamical laws could not explain the non-linear processes he saw in weather data. This made a non-linear theory necessary.

Deterministic Chaos

Chaos theory is the study of systems that are highly sensitive to initial conditions.

It is important to stress that there is nothing random or undetermined about chaos theory. It involves no quantum indeterminacy, which is the basis for ontological chance. Although it exhibits behaviors that resemble some phenomena in the real world, they are metaphors for behaviors, not physical explanations.

Chaos should not be confused with unpredictability, just as determinism should not be confused with predictability. The fundamental importance of chaos theory is its application to systems that are extremely sensitive to initial conditions. Chaotic systems are deterministic, but not predictable. Their unpredictability does not mean that they are random or indeterministic, as many philosophers and a few scientists who dislike quantum mechanics have mistakenly believed (e.g., Ilya Prigogine).

Some philosophers appear to believe that chaos theory can provide all the randomness need to prevent free will from being deterministic (e.g., Daniel Dennett). Some think that non-linear chaotic behavior disproves the determinism of Laplace's super-intelligent demon. Laplace probably knew that the information required by the demon was unobtainable. Isaac Newton certainly knew that his observations could not confirm his theory to arbitrary accuracy needed to prove perfect determinism.

Ludwig Boltzmann, his admirer and contemporary Franz Exner, and Exner's student Erwin Schrödinger, often pointed out that deterministic theories go beyond the available evidence. Popularization of physical theories has often confused not just the public, but even philosophers of science.

On the three hundredth anniversary of Newton’s
Principia, Sir James Lighthill gave a lecture to the Royal Society, lamenting the confusion between Newton's classical mechanical determinism and the apparent claim of perfect predictability:

”We are all deeply conscious today that the enthusiasm of our forebears for the marvellous achievements of Newtonian mechanics led them to make generalizations in this area of predictability which, indeed, we may have generally tended to believe before 1960, but which we now recognize were false. We collectively wish to apologize for having misled the general educated public by spreading ideas about determinism of systems satisfying Newton’s laws of motion that, after 1960,
were to be proved incorrect...”

(J. Lighthill, Proc. Roy. Soc. (London) A 407, 35 (1986))

Sensitivity to initial conditions was in fact known long before modern chaos theory and complexity theory. James Clerk Maxwell noted in the 1860's that even if two molecules were adjacent to one another in a hydrodynamic flow, they might find themselves in random places in the container after relatively short mixing times. He wrote:

When the state of things is such that an infinitely small variation of the present state will alter only by an infinitely small quantity the state at some future time, the condition of the system, whether at rest or in motion, is said to be stable; but when an infinitely small variation in the present state may bring about a finite difference in the state of the system in a finite time, the condition of the system is said to be unstable.

Maxwell may have been first, but certainly not the last, to connect this sensitivity to initial conditions to free will (e.g., John Eccles, with his "critically poised neurons.")

The real world is only approximately classical mechanical (obeying Newton's dynamical laws at all scales). At the small scales of atomic and molecular physics, the world is quantum mechanical. There is nothing corresponding to deterministic chaos in quantum physics. Deterministic chaos requires continuous motion to produce mathematical singularities and exponential non-linearity.

Despite their unpredictable and spontaneous "quantum jumps," the discrete states of the quantum world are more regular and stable than their classical analogues. Indeed, the long-term stability of quantum structures in their "ground states" is astonishing, as is the complete indistinguishability of elementary particles, which gives rise to extremely non-intuitive statistics. Finally, the long-term stability of quantum cooperative phenomena is evident in the ability of biological macromolecules to maintain (by error detection and correction) their information content over billions of years.

The desire to describe randomness and chance in the world with deterministic chaos resembles the view of Adolphe Quételet and Henry Thomas Buckle that statistical regularities in various physical and social phenomena are evidence of an underlying determinism. Is the motivation similar to that which seeks an intelligent designer behind biological evolution? It seems that the "antipathy to chance" observed by William James at the end of the nineteenth century is alive and well in the twenty-first.

The Santa Fe Institute

Scholars at the Santa Fe Institute promote the self-organization aspects of complexity and chaos theories as assisting Darwin's theory of evolution. There is no doubt that in the early stages between non-living and living systems that auto-catalytic molecular evolution might provide one of the steps to biogenesis.

But some of these scholars think that complexity theory adds something that is not provided by the randomness of quantum physics. It may, but it does not provide the purpose (the teleonomy or entelechy) that appears when molecules first discover how to replicate themselves. And more important, it does not add any teleological purpose that pre-exists life.

Physical systems far from equilibrium use the flow of matter and energy from the environment through an open system to create and maintain information structures. In this respect, they resemble living systems, whaich are information structures, patterns, through which matter and energy flows. They do produce Prigogine's "order from chaos." But they are not information replicators and the information processors that evolve from the simplest organisms.

Atomic constraints such as the quantum-mechanical bonding of water molecules allow snow crystals to self-organize into spectacular forms, producing order from disorder. Besides crystals, there are whirlpools, Bénard convection cells, basalt columns, and soil polygons, all of which apparently violate the fundamental tendency toward equilibrium and disorder in the universe. These are processes that information philosophy calls ergodic. They can do this only because of the negative entropy flow from the Sun. They all are completely undirected and purposeless, like the formation of the galaxies, stars, and planets. They cannot add meaning to the universe.

Stuart Kauffman is perhaps the best known exponent of complexity as aiding natural selection.

The
origin of life, rather than having been vastly improbable, is instead an expected collective
property of complex systems of catalytic polymers and the molecules on which
they act. Life, in a deep sense, crystallized as a collective self-reproducing metabolism
in a space of possible organic reactions. If this is true, then the routes to life are many
and its origin is profound yet simple.

While heretical, this new body of theory is robust in the sense that the conclusions
hold for a wide variety of assumptions about prebiotic chemistry, about the kinds of
polymers involved, and about the capacities of those polymers to catalyze reactions
transforming either themselves or other, very similar polymers. It is also robust in
leading to a fundamental new conclusion: Molecular systems, in principle, can both
reproduce and evolve without having a genome in the familiar sense of a template-replicating
molecular species. It is no small conclusion that heritable variation, and
hence adaptive evolution, can occur in a self-reproducing molecular system lacking a
genome. Since Darwin's theory of evolution, Mendel's discovery of the "atoms" of
heredity, and Weismann 's theory of the germ plasm, biologists have argued that evolution
requires a genome. False, I claim.

(The Origins of Order, 1993, p.285)

Kauffman's ideas about autocatalytic systems are shared by Terrence Deacon.

Kauffman thought that he might even discover "laws" of self-organization. In his 1995 book, At Home in the Universe, he identified the discovery of such laws as showing that human life followed directly from these pre-existing laws, which would replace the arbitrary and purposeless system of Darwinian natural selection.